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Poster
Chefs' Random Tables: Non-Trigonometric Random Features
Valerii Likhosherstov · Krzysztof M Choromanski · Kumar Avinava Dubey · Frederick Liu · Tamas Sarlos · Adrian Weller

Thu Dec 01 09:00 AM -- 11:00 AM (PST) @ Hall J #542
We introduce chefs' random tables (CRTs), a new class of non-trigonometric random features (RFs) to approximate Gaussian and softmax kernels. CRTs are an alternative to standard random kitchen sink (RKS) methods, which inherently rely on the trigonometric maps. We present variants of CRTs where RFs are positive, a key requirement for applications in recent low-rank Transformers. Further variance reduction is possible by leveraging statistics which are simple to compute. One instantiation of CRTs, the optimal positive random features (OPRFs), is to our knowledge the first RF method for unbiased softmax kernel estimation with positive and bounded RFs, resulting in exponentially small tails and much lower variance than its counterparts. As we show, orthogonal random features applied in OPRFs provide additional variance reduction for any dimensionality $d$ (not only asymptotically for sufficiently large $d$, as for RKS). We test CRTs on many tasks ranging from non-parametric classification to training Transformers for text, speech and image data, obtaining new state-of-the-art results for low-rank text Transformers, while providing linear space and time complexity.

#### Author Information

##### Adrian Weller (Cambridge, Alan Turing Institute)

Adrian Weller is Programme Director for AI at The Alan Turing Institute, the UK national institute for data science and AI, where he is also a Turing Fellow leading work on safe and ethical AI. He is a Principal Research Fellow in Machine Learning at the University of Cambridge, and at the Leverhulme Centre for the Future of Intelligence where he is Programme Director for Trust and Society. His interests span AI, its commercial applications and helping to ensure beneficial outcomes for society. He serves on several boards including the Centre for Data Ethics and Innovation. Previously, Adrian held senior roles in finance.